[BUG]: ddtrace breaks applications with OpenAI usage

[vilmar-hillow]

Tracer Version(s)

4.0.0

Python Version(s)

3.13.2

Pip Version(s)

N/A

Bug Report

It seems like when running an application that initializes an OpenAI client with function as an api key isn't possible, even with no LLM observability explicitly enabled.

Expected behaviour:

• ddtrace doesn't block the application from running, especially with no LLM observability configured explicitly.

Reproduction Code

import logging

import azure.identity
import openai

logging.basicConfig(level=logging.ERROR)

OPENAI_AZURE_URL = "https://foo.openai.azure.com/openai/v1/"
OPENAI_MODEL = "gpt-4.1-nano"

token_provider = azure.identity.get_bearer_token_provider(
    azure.identity.AzureCliCredential(),
    "https://cognitiveservices.azure.com/.default",
)

client = openai.OpenAI(base_url=OPENAI_AZURE_URL, api_key=token_provider)

Run with ddtrace-run python sample.py or DD_LLMOBS_ENABLED=false ddtrace-run python sample.py

Error Logs

Traceback (most recent call last):
  File "/home/.../test_ddtrace_fail.py", line 16, in <module>
    client = openai.OpenAI(base_url=OPENAI_AZURE_URL, api_key=token_provider)
  File "/home/.../.venv/lib/python3.13/site-packages/ddtrace/contrib/internal/trace_utils.py", line 315, in wrapper
    return func(mod, pin, wrapped, instance, args, kwargs)
  File "/home/.../.venv/lib/python3.13/site-packages/ddtrace/contrib/internal/openai/patch.py", line 200, in patched_client_init
    integration.user_api_key = api_key
    ^^^^^^^^^^^^^^^^^^^^^^^^
  File "/home/.../.venv/lib/python3.13/site-packages/ddtrace/llmobs/_integrations/openai.py", line 60, in user_api_key
    self._user_api_key = "sk-...%s" % value[-4:]
                                      ~~~~~^^^^^
TypeError: 'function' object is not subscriptable

Libraries in Use

ddtrace==4.0.0
openai==2.9.0
azure-identity==1.25.1

Operating System

Ubuntu 24.04